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    <title>%sn</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>%sn</b> -  Jacobi 's elliptic function</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[y]=%sn(x,m)  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>x</b>
        </tt>: a point inside the fundamental rectangle  defined by the elliptic integral; <tt>
          <b>x</b>
        </tt> is a vector of complex numbers</li>
      <li>
        <tt>
          <b>m</b>
        </tt>: parameter of the elliptic integral (<tt>
          <b>0&lt;m&lt;1</b>
        </tt>)</li>
      <li>
        <tt>
          <b>y</b>
        </tt>: result</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    Jacobi 's sn elliptic function with parameter <tt>
        <b>m</b>
      </tt>: the inverse 
    of the elliptic integral for the parameter <tt>
        <b>m</b>
      </tt>.</p>
    <p>
    The amplitude am is computed in fortran and 
    the addition formulas for elliptic functions are applied</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

m=0.36;
K=%k(m);
P=4*K; //Real period
real_val=0:(P/50):P;
plot(real_val,real(%sn(real_val,m)))
xbasc();
KK=%k(1-m);
Ip=2*KK;
ima_val1=0:(Ip/50):KK-0.001;
ima_val2=(KK+0.05):(Ip/25):(Ip+KK);
z1=%sn(%i*ima_val1,m);z2=%sn(%i*ima_val2,m);
plot2d([ima_val1',ima_val2'],[imag(z1)',imag(z2)']);
xgrid(3)
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="percentasn.htm">
        <tt>
          <b>%asn</b>
        </tt>
      </a>,&nbsp;&nbsp;<a href="percentk.htm">
        <tt>
          <b>%k</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>F. D.  </p>
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